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Finite amplitude instability of time-dependent flows

Published online by Cambridge University Press:  29 March 2006

Stephen H. Davis
Stephen H. Davis*
Affiliation:
Mechanics Department, The Johns Hopkins University
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Abstract

An extension of the StuartWatson technique for examination of the non-linear hydrodynamic instability of time-dependent flows is proposed. An example in Bnard convection is used to illustrate the method. Extensions to more general problems are indicated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 45 , Issue 1 , 15 January 1971 , pp. 33 - 48
Copyright
Copyright © Cambridge University Press 1971

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References

Coddington, E. A. & Levinson, N. 1955 Theory of Ordinary Differential Equations. New York: McGraw-Hill.Google Scholar
Conrad, P. W. & Criminale, W. O. 1965a Z. angew. Math. Phys. 16, 233.Google Scholar
Conrad, P. W. & Criminale, W. O. 1965b Z. angew. Math. Phys. 16, 569.Google Scholar
Currie, I. G. 1967 J. Fluid Mech. 29, 337.Google Scholar
Davis, S. H. 1969a Proc. Roy. Soc. A, 310, 341.Google Scholar
Davis, S. H. 1969b Proc. IUTAM Symp. on Instability of Continuous Systems, Herrenalb.Google Scholar
Eckhaus, W. 1965 Studies in Non-linear Stability Theory. New York: Springer.10.1007/978-3-642-88317-0CrossRefGoogle Scholar
Foster, T. D. 1965a Phys. Fluids, 8, 1249.Google Scholar
Foster, T. D. 1965b Phys. Fluids, 8, 1770.Google Scholar
Gresho, P. & Sani, R. L. 1970 J. Fluid Mech. 40, 783.Google Scholar
Gresho, C. E. & Salwen, H. 1968 J. Fluid Mech. 34, 177.Google Scholar
Joseph, D. D. 1965 Arch. Rat. Mech. Anal. 20, 59.Google Scholar
Joseph, D. D. 1966 Arch. Rat. Mech. Anal. 22, 163.Google Scholar
Lick, W. 1965 J. Fluid Mech. 21, 565.Google Scholar
Morton, B. R. 1957 Quart. J. Mech. Appl. Math. 10, 433.Google Scholar
Robinson, J. L. 1967 J. Fluid Mech. 29, 461.Google Scholar
Rosenblat, S. 1968 J. Fluid Mech. 33, 321.Google Scholar
Segel, L. A. 1962 J. Fluid Mech. 14, 97.Google Scholar
Segel, L. A. 1965 J. Fluid Mech. 21, 345.Google Scholar
Segel, L. A. 1966 Non-equilibrium Thermodynamics, Variational Techniques, and Stability (Donnelly, R., Herman, R., and Prigogine, I., eds.), University Chicago Press, 1962.Google Scholar
Segel, L. A. & Stuart, J. T. 1962 J. Fluid Mech. 13, 289.Google Scholar
Shen, S. F. 1961 J. Aero. Sci. 28, 397.Google Scholar
Stuart, J. T. 1960a J. Fluid Mech. 9, 353.Google Scholar
Stuart, J. T. 1960b Proc. Xth Int. Cong. Appl. Mech., Stresa.Google Scholar
Venezian, G. 1969 J. Fluid Mech. 35, 243.Google Scholar
Watson, J. 1960 J. Fluid Mech. 9, 371.Google Scholar
Yih, C-S. 1968 J. Fluid Mech. 31, 737.Google Scholar